Spinphase

Spinphase refers to the instantaneous rotational phase of a spinning object, typically defined modulo 2π or in cycles. In pulsar astronomy and related fields, spin phase is the primary coordinate used to describe where a rotating body is in its cycle at a given time, and it serves as the basis for folding time-series data to reveal periodic signals.

Mathematically, the phase φ(t) is related to the spin frequency ν(t) = dφ/dt. If one adopts a reference epoch t0 with phase φ0, the phase at time t is φ(t) = φ0 + ∫ from t0 to t ν(t′) dt′. When expressed in cycles, ψ(t) = φ(t)/(2π) and ψ̇(t) = ν(t). In practice, the phase is often treated modulo 1 (a full cycle) for convenience. The spin frequency itself may change slowly over time (spin-down) or experience abrupt changes (glitches), and higher derivatives (ν̇, ν̈, etc.) are sometimes needed for accuracy.

In pulsar timing, the phase model combines spin evolution with other effects such as orbital motion, proper motion, and propagation delays. Observed arrival times of pulses (TOAs) are transformed to a common reference frame, and the phase model is used to "fold" data to construct stable pulse profiles. Phase-coherent timing aims to maintain a continuous phase connection across observations, enabling precise measurements of rotational behavior and testing of fundamental physics.

Beyond pulsars, spin phase is a general term for the angle of rotation of any rigid body as a function of time, central to rotational dynamics, control systems, and signal processing. The conventions for reference phase, units (radians or cycles), and time frames vary by context.